David E. Weeks

Rotation–vibration spectra of icosahedral molecules. II. Icosahedral symmetry, vibrational eigenfrequencies, and normal modes of buckminsterfullerene

The icosahedral symmetry of molecules such as buckyball, B12H12−2, and C20H20, is analyzed using subgroup chain defined projection operators. The icosahedral analysis is used to determine the eigenvalues and eigenvectors of a classical spring mass model of buckyball. A spectrum of Raman and dipole active modes is given using the spring constants of benzene. Corresponding dipole active and Raman active normal modes are displayed stereographically. Several choices for springs constants are discussed and a comparison with spring mass systems of reduced symmetry is made.

Wave packet correlation function formulation of scattering theory: The quantum analog of classical S‐matrix theory

A novel time‐dependent quantum mechanical formulation of scattering theory is developed which is well suited for the calculation of individual S‐matrix elements. Wave packets corresponding to well‐defined reactant and product channel quantum numbers are propagated in to the interaction region using Mo/ller operators, the former forward in time and the latter backwards in time. The S‐matrix element Sβα(E) is then simply related to the Fourier transform at energy E of the time‐dependent correlation function between the two wave packets in the interaction region. The symmetric treatment of reactants and products allows the entrance and exit channel dynamics to be performed highly efficiently using different coordinate systems and different interaction representations. As a result, the formulation is expected to provide an improved route to the calculation of S‐matrix elements using quantum mechanical, as well as semiclassical propagation methods. The new formulation combines elements of classical S‐matrix th...

Vibrational frequencies and normal modes of buckminsterfullerene

Abstract Icosahedral symmetry analysis is used to determine the eigenvalues and eigenvectors of a classical spring mass model of Buckyball. Several choices for spring constants are discussed and a comparison with spring mass systems of reduced symmetry is made. Dipole active normal modes are displayed stereographically.

Rotation–vibration spectra of icosahedral molecules. I. Icosahedral symmetry analysis and fine structure

Icosahedral symmetry analysis is developed for analyzing eigensolutions of rovibrational tensor Hamiltonians for molecules such as B12H12−2, C20H20, and C60. Simplified asymptotic formulas and procedures are developed for obtaining rotational spectral fine structure for high angular momentum. J=100 eigenlevels for sixth‐ and tenth‐rank icosahedral tensors are discussed using different approximations and visualization schemes.

Photoelectron spectroscopy of Si2C3− and quantum chemistry of the linear Si2C3 cluster and its isomers

The 364 nm photoelectron spectrum of Si2C3− is reported, together with high level ab initio calculations of the linear anion, and six linear and eight nonlinear structures of the neutral Si2C3. The adiabatic electron affinity of Si2C3, corresponding to the transition from the linear anion to the lowest electronic state of the linear singlet neutral, is found to be 1.766±0.012 eV. Theoretical results were essential for interpreting the spectrum. The level of theory necessary to accurately describe the electronic structure of Si2C3 cluster isomers is presented and discussed. Several vibration frequencies for the neutral linear structure are obtained from the spectra and compared to results from different levels of theory.

Rovibrational spectral fine structure of icosahedral molecules

Abstract Predictions are made for possible spectral patterns in rovibronic fine structure in high-resolution spectra of icosahedrally symmetric molecules. Qualitative and semi-quantitative features are discussed which might help in identifying and assigning a complex spectrum. Interpretation of some features are made in terms of quantum and semi-classical dynamics.

Rotation—vibration scalar coupling χ coefficients and spectroscopic band shapes of buckminsterfullerene

Abstract The Maxwell—Boltzmann distribution is used to calculate J max for the proposed icosahedrally symmetric structure of C 60 called buckminsterfullerene. The results are used with calculated rotation—vibration scalar coupling χ coefficients to make predictions for the dipole active rovibrational band shapes. Stereoscopic figures of the corresponding normal modes are shown in the body fixed rotating frame. Rotational constants and spectral features of CH 4 , CF 4 , and SF 6 are included for comparison.

M + Ng potential energy curves including spin-orbit coupling for M = K, Rb, Cs and Ng = He, Ne, Ar

The X(2)Σ(1/2)(+), A(2)Π(1∕2), A(2)Π(3∕2), and B(2)Σ(1/2)(+) potential energy curves and associated dipole matrix elements are computed for M + Ng at the spin-orbit multi-reference configuration interaction level, where M = K, Rb, Cs and Ng = He, Ne, Ar. Dissociation energies and equilibrium positions for all minima are identified and corresponding vibrational energy levels are computed. Difference potentials are used together with the quasistatic approximation to estimate the position of satellite peaks of collisionally broadened D2 lines. The comparison of potential energy curves for different alkali atom and noble gas atom combinations is facilitated by using the same level of theory for all nine M + Ng pairs.

High Tc superconducting levitation motor with a laser commutator. II

Significant improvements and extensions have been made to a high Tc superconducting levitation motor with an optical commutator. The primary extension is the development of a heat exchanger that permits high Tc superconductors to be cooled with liquid nitrogen to 77 K and below in vacuums of 10−5 Torr and less. This permits the levitation motor to be operated without the decelerating force of atmospheric drag. The result is an increase of nearly two orders of magnitude in the sustainable rotational frequency from a maximum of 10 s−1 at atmospheric pressure to 500 s−1 (30 000 rpm) at 10−5 Torr. The corresponding tangential velocity of the rotor arms increased from 3 m/s to 155 m/s. Angular frequencies between 100 s−1 and 200 s−1 have been sustained for periods exceeding 6 h. Measurements and analysis of rotor deceleration as a function of pressure and time are presented. Other improvements are discussed.

A torsion balance to measure hysteretic levitation forces in high Tc superconductors

A simple torsion balance is described which is used to measure the levitation force on a magnet as a function of height above bulk samples of the new high Tc superconductors. Results are presented for a the YBa2Cu3Ox (Tc∼90 K) and the Tl‐Ba‐Ca‐Cu‐O (Tc∼120 K) superconducting systems. Possible uses for the balance are discussed.